Modern nucleic acid sequencing methods have provided a vast wealth of genetic sequence data and will continue to do so. The analytical analyses of these data have led to an increase in understanding in such areas as genetic regulation, dependence of molecular function and structure on sequence, genotypic variability, and molecular evolution and taxonomy. Our understanding of these analyses has recently been elevated to the level of rigorous mathematics, allowing the careful investigation of current ideas and interpretations as well as the rigorous testing of new suppositions on this vast data set. The primary aims of the work to be carried out under this proposal are: to continue the development of the genetic sequence comparative methods; to investigate and understand their mathematical properties; to investigate and expand their applicability to the current problems of molecular biology, with particular emphasis on generalizing the homology algorithms to include the general physical-chemical interactions and constraints involved in gene expression. In order to effectively carry out these aims, the current cooperative interplay with the experimental molecular biological community will be expanded, and a mechanism for the exchange of improved analysis tools will be developed.